Books by and about F. W. Lanchester. What are Lanchester's Equations? Lanchester's Linear Law is an equation of combat that relates to individual confrontations between soldiers where the outcome is dependent on the ratio of weapon efficiency (E) of the individual combatants and the combat strength of the army = E (number of troops). The outcome of the battle is the difference between the original troop numbers. Lanchester's N-Squared Law says that in mechanized warfare with modern weapons, each soldier can attack multiple targets but is also subject to incoming fire from many directions. In this case the attrition rate is proportional to the number of troops on the opposing side. The solution to the first order differential equation leads to Lanchester's Second Law: combat strength of the army = E (number of troops squared), also called Lanchester's N-Squared Law. Lanchester's Principle of Concentration: the basis of this strategy is concentration of the main strength of force at one point in the field of operations. With modern long-range weapons, the concentration of firepower gives an immediate superiority to which the inferior force cannot respond in like terms. This means that the superior force should always choose to fight under N-Squared Law conditions....